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4024/22 May/Jun 2020, Question 3: Choosing the Right Trigonometric Ratio

Cambridge O Level Mathematics 4024 · Paper 22 (Calculator) · Calculator · 6 marks

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The question, in short

Using a light 8 m above ground point B, find angles and lengths involving points P, Q and a 1.6 m pole casting shadow TS, with PB = 12 m, ladder angle 70°, TB = 6.5 m.

Summarised in our own words. Use the official paper for the exact wording and the diagram.

Part (a) · 2 marks

Calculate the angle of elevation of the light L from point P, where P is 12 m horizontally from B.

  1. 1tan P = 8/12
  2. 2Angle of elevation = tan⁻¹(8/12) = 33.69… ≈ 33.7°

Answer33.7 or 33.69…

Part (b) · 2 marks

Calculate the ladder length QL, given the ladder reaches L and makes 70° with the ground.

  1. 1sin 70° = 8/QL
  2. 2QL = 8 ÷ sin 70° = 8.513… ≈ 8.51 m

Answer8.51 or 8.513…

Part (c) · 2 marks

Calculate the shadow length TS of the 1.6 m vertical pole, given LRT is straight and TB = 6.5 m.

  1. 1Triangles TSR and TBL are similar
  2. 2TS/6.5 = 1.6/8
  3. 3TS = 6.5 × 1.6 ÷ 8 = 1.3 m

Answer1.3

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